As a vector bottomonium candidate [1]}, the recently reported \(\Upsilon (10753)\)  by Belle exists in the \(e^+e^-\rightarrow \Upsilon (nS)\pi ^+\pi ^-\)  (\(n=1,2,3\) ) processes [2]}. The \(\Upsilon (10753)\)  is a crucial state when constructing the bottomonium family. The study of its hidden-bottom decays is an important aspect to reflect the spectroscopy behavior of the \(\Upsilon (10753)\)  [3]}, [4]}. In this work, we calculate the \(\Upsilon (10753)\rightarrow \Upsilon (1^3D_J)\eta \)  decays, which are involved in the observed
\(\Upsilon (1^3D_2)\)  [5]} and two missing bottomonia \(\Upsilon (1^3D_1)\)  and \(\Upsilon (1^3D_3)\) . Since the coupled-channel effect cannot be ignored for higher bottomonia [1]}, we should introduce the hadronic loop mechanism when exploring the decay behavior of the \(\Upsilon (10753)\rightarrow \Upsilon (1^3D_J)\eta \)  decays, and find that the \(\Upsilon (10753)\rightarrow \Upsilon (1^3D_1)\eta \)  and \(\Upsilon (10753)\rightarrow \Upsilon (1^3D_2)\eta \)  decay channels have sizable branching ratios. Thus, it is possible to find out these two predicted decay modes at Belle II. Different from these two decay channels, the
\(\Upsilon (10753)\rightarrow \Upsilon (1^3D_3)\eta \)  decay is suppressed. Thus, searching for \(\Upsilon (10753)\rightarrow \Upsilon (1^3D_3)\eta \) 
is not promising only if more data are accumulated in experiments.
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